Unitary Interpolants and Factorization Indices of Matrix Functions

摘要

For an n x n bounded matrix function phi the authors study interpolants U, i.e.,211u001eunitary-valued functions U. The authors are looking for unitary interpolants U 211u001efor which the Toeplitz operator Tu is Fredholm. The authors give a new approach 211u001ebased on superoptimal singular values and thematic factorizations. The authors 211u001egive a new approach based on superoptimal singular values and thematic 211u001efactorizations. The authors describe Weiner-Hopf factorization indices of U in 211u001eterms of superoptimal singular values of phi and thematic indices of phi-F, where 211u001eF is a superptimal approximation of phi by bounded analytic matrix functions. The 211u001eapproach essentially relies on the notion of a monotone thematic factorization 211u001eintroduced in (AP). In the last section the authors discuss hereditary properties 211u001eof unitary interpolants.